Appurtenances (from late Latin appertinentia, from appertinere, "to appertain") is a legal term for what belongs to and goes with something else, the accessories or things usually conjoined with the substantive matter in question.
In Gestalt theory, appurtenance (or "belongingness") is the relation between two things seen which exert influence on each other. For example, fields of color exert influence on each other. "A field part x is determined in its appearance by its 'appurtenance' to other field parts. The more x belongs to the field part y, the more will its whiteness be determined by the gradient xy, and the less it belongs to the part z, the less will its whiteness depend on the gradient xz."1
References
1Koffa (1935) p246 qtd in Gilchrist (Seeing Black and White p. 63)
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